The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor being present in air. Like any liquid, water has a tendency to evaporate. As it does, particles of gaseous water become mixed in the air. This additional matter will affect the mass density of the air (an inertial property). The temperature will affect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:

4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C.

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Focal length

The simplest way to find the focal length of a lens is to look at its specifications. Most lenses have the focal length marked directly on them. For prime lenses, it will be a single number (e.g., 50mm), while zoom lenses will show a range (e.g., 24-70mm).

A lens focal length combines various elements that help to focus the light and minimize distortions. The location where all the light rays converge to form a sharp image is known as the optical center of the lens.

With ten years under my belt as a professional photographer, I've found that telephotos are better than wide for my work — here's why.

In short, they help photographic subjects appear closer than they are, achieving a beautiful compression for that desirable blurred background. There is a wide range of telephoto lenses on the market, including:

Additionally, the larger size of full-frame sensors allows for better low-light performance and less noise at high ISO settings, enhancing image quality in challenging lighting conditions.

Lastly, fisheye lens are a super fun addition to the camera bag if you’re into the widest view possible. Their angle of view is usually 180°, allowing you to see half of a full rotation and offering a distinctive, hemispherical lens distortion. They cram in as much information as possible; thus, they don’t produce straight lines. These are awesome for creative, experimental photography projects, especially within fashion portraits or skateboarding content.

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 10 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

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8. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls?

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While an echo is of relatively minimal importance to humans, echolocation is an essential trick of the trade for bats. Being a nocturnal creature, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves that reflect off objects in their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses. These bats are utilizing the physics of the Doppler effect discussed in an earlier unit (and also to be discussed later in Lesson 3). This method of echolocation enables a bat to navigate and to hunt.

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 256 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

Focal lengthcamera

Prime lenses are usually more compact and lighter than zoom lenses, making them convenient for travel and long shooting sessions. Their smaller size and weight are due to the absence of the extra glass and mechanics needed for zooming.

The speed of the sound wave at this temperature is 343 m/s (using the equation described in the Tutorial). The distance can be found using d = v • t resulting in an answer of 343 m. Use 0.61 second for the time since 1.22 seconds refers to the round-trip distance.

6. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.

Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is

A wide-angle lens is often characterized by a focal length of 35mm or shorter, giving the photographer a wide field of view. The wider your field of view, the more of the scene you'll effortlessly capture in the frame. These lenses are ideal for many scenarios, and most photographers have at least one trusty wide-angle lens in their kit. If you’re a beginner photographer or want the first lens for a camera camera, it’s wise to go with a nifty 35mm lens focal length.

At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and the lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 20 000 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

2. On a hot summer day, a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second.

On the other hand, the smaller APS-C sensors come with a "crop factor" of about 1.5x to 1.6x, effectively increasing the focal length of lenses and providing extra "reach," which can be beneficial for telephoto photography such as sports or wildlife. Despite potentially higher noise levels in low light, APS-C cameras offer a more compact and affordable option for those seeking a balance between performance and portability. This makes them attractive to amateurs, enthusiasts, and even professionals who value a lighter system.

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Generally, choosing a long focal length lens, like 70mm, 135mm, or 200mm, is wise to isolate textures and distant features to create dramatic backgrounds. Wide focal length lenses, like 16mm, 24mm, or 35mm, thrive when you want the entire scene in focus, like when shooting simple landscapes with long leading lines.

1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object?

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Like any wave, a sound wave has a speed that is mathematically related to the frequency and the wavelength of the wave. As discussed in a previous unit, the mathematical relationship between speed, frequency and wavelength is given by the following equation.

An imager that collects visible light (400 to 700nm) and converts it to a color image that replicates normal human vision.

The above equation is useful for solving mathematical problems related to the speed, frequency and wavelength relationship. However, one important misconception could be conveyed by the equation. Even though wave speed is calculated using the frequency and the wavelength, the wave speed is not dependent upon these quantities. An alteration in wavelength does not affect (i.e., change) wave speed. Rather, an alteration in wavelength affects the frequency in an inverse manner. A doubling of the wavelength results in a halving of the frequency; yet the wave speed is not changed. The speed of a sound wave depends on the properties of the medium through which it moves and the only way to change the speed is to change the properties of the medium.

Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property. The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. As stated above, sound waves travel faster in solids than they do in liquids than they do in gases. However, within a single phase of matter, the inertial property of density tends to be the property that has a greatest impact upon the speed of sound. A sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium than it will in air. This is mostly due to the lower mass of Helium particles as compared to air particles.

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Then there's the standard lens, around 50mm, often hailed as the "nifty fifty." It’s akin to the human eye in how it captures the world, making it incredibly versatile. It’s perfect for everyday shooting and portraits, blending background and foreground elements naturally. As a beginner, using a 50mm lens encourages you to physically move around, engaging more with your environment, which can lead to more thoughtful compositions.

Let’s break it down: Wide-angle lenses (under 35mm) are your go-to for capturing vast landscapes and bustling street scenes. They fit more into the frame, which is great for sweeping views and architectural photography. Meanwhile, telephoto lenses (over 70mm) excel in bringing distant subjects into sharp relief. They're ideal for zeroing in on distant details, perfect for sports or wildlife photography, and they add a dramatic flair by compressing space, making elements in the photo appear closer together.

A catadioptric system merges the strengths of both refractive (lens-based) and reflective (mirror-based) elements to create powerful and versatile optical ...

The differences between cropped (APS-C) and full-frame sensors are significant in digital photography, influencing various aspects of image quality, field of view, depth of field, and camera system size and cost.

Remember that all focal lengths depend entirely on the photographer’s vision or personal preference. Like all art forms, there are no steadfast rules to abide by. This article is merely a guideline for the purpose of each focal length, including some technical differences between the various offerings you see today.

While there is a broad range of pricing for prime lenses, they can be less expensive than zoom lenses of comparable quality, especially at wider apertures. This cost-effectiveness stems from the more straightforward construction and fewer materials required.

homogeneity of variance – -

5. Most people can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to this upper range of audible hearing.

Let = wavelength. Use v = f • λ where v = 350 m/s and f = 600 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

Prime lenses are the unsung heroes of the photography world. Fixed in focal length, they don't have the zoom capabilities of their counterparts, but what they lack in flexibility, they make up for in quality. Because they contain fewer glass elements, prime lenses can capture images that are not only sharper but also more vibrant.

The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period of time.

The speed of the sound wave is 340 m/s. The distance can be found using d = v • t resulting in an answer of 25.5 m. Use 0.075 seconds for the time since 0.150 seconds refers to the round-trip distance.

Focal length inphotography

The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.

Any 24mm and 16mm lens is an excellent option if you want something extra wide. Focal lengths below 16mm are considered ultra-wide angles.

Strictly, the Principal Distance is the distance mentioned above (i.e. distance from imaging plane to the lens optical sensor), and the focal length is the ...

The canyon wall is 242 meters away. You might have noticed that the time of 0.70 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.

Focaldistance vsfocal length

Focal length might sound technical, but it's really your secret weapon in framing the perfect shot. It's measured in millimeters and determines not just the angle of view—how much of your scene is captured—but also how your images are magnified. As a beginner, understanding this can transform the way you approach photography.

If the lens marking is unclear or you want more details, the lens manual or the manufacturer's website will provide specifications, including the focal length.

They typically have larger maximum apertures (e.g., f/1.4, f/1.8, f/2.8), allowing more light to reach the sensor. This makes them excellent for low-light situations and for achieving shallow depth-of-field effects where the subject is in sharp focus against a smoothly blurred background.

Doubling the frequency will halve the wavelength; speed is unaffected by the alteration in the frequency. The speed of a wave depends upon the properties of the medium.

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10. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.

The most popular wide-angle zoom range is 16-35mm. Most kit or standard zoom lenses go down to 24mm or28mm. The widest lenses on the market are 10mm (rectilinear) and 8mm (fisheye).

Long-focal length lenses range in the 100-600+ range and appear to bring far away objects close to the camera. Made swimmingly for the landscape photographers in mind, long lengths are perfect for wildlife, the bird on the backyard feeder, the child at the top of a water slide, or athletes on the other side of the football field. Lenses longer than 70mm focus on infinity after 100 feet. This infinity-focusing distance means a couple of different things.

Beyond the technical benefits, using a prime lens influences your creative process. Without the ability to zoom, you’re encouraged to physically move around your subject to compose the perfect shot. This often results in more thoughtful framing and a better connection with your subject. Whether you’re shooting portraits, street scenes, or landscapes, a prime lens can push you to explore new perspectives and enhance your compositional skills.

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Explore the world in creative new ways with exceptional G Master performance in a 16-35mm F2.8 wide-angle zoom. This lens delivers consistently superb resolution from corner-to-corner, no matter what ...

Wide-angle camera lenses are a fan-favorite among most lifestyle bloggers and everyday shooters; they’re perfect for capturing an entire scene and confined spaces if you want to show how the entire bedroom looks or the whole restaurant with the crowds of customers — the shorter focal length lens will be your best bet.

FOV tofocal length

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9. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The velocity of wave B must be __________ the velocity of wave A.

The magic of a prime lens lies in its simplicity. The straightforward optical design enhances light transmission, allowing for incredibly clear and precise images. This can make a noticeable difference in your photography, especially when shooting in low light conditions. Moreover, with minimal distortion and chromatic aberration, your photos will have a professional sleekness that’s hard to achieve with a standard zoom lens.

Getting into the art of photography? Just upgraded to a new camera body and need to decide which lens to purchase? Finding the right lens for your needs depends entirely on the focal length. Are you shooting portraits, weddings, sports, or wildlife? Street? Food?

(The above equation relating the speed of a sound wave in air to the temperature provides reasonably accurate speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)

Since Wave B has three times the wavelength of Wave A, it must have one-third the frequency. Frequency and wavelength are inversely related.

The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity. (Elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed (v) of a wave, thus yielding this general pattern:

A sound wave is a pressure disturbance that travels through a medium by means of particle-to-particle interaction. As one particle becomes disturbed, it exerts a force on the next adjacent particle, thus disturbing that particle from rest and transporting the energy through the medium. Like any wave, the speed of a sound wave refers to how fast the disturbance is passed from particle to particle. While frequency refers to the number of vibrations that an individual particle makes per unit of time, speed refers to the distance that the disturbance travels per unit of time. Always be cautious to distinguish between the two often-confused quantities of speed (how fast...) and frequency (how often...).

Lens compatibility is another consideration; full-frame lenses can be used on both sensor types, but APS-C lenses on full-frame bodies may result in vignetting. Finally, while full-frame cameras are more expensive, they are preferred for their superior image quality and flexibility in various shooting conditions. Conversely, due to the crop factor, APS-C cameras are favored for their affordability, compactness, and built-in telephoto advantage, making them a versatile choice for many photographers.

Another phenomenon related to the perception of time delays between two events is an echo. A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 1.40 seconds after making the holler, then the distance to the canyon wall can be found as follows:

Focal length in photography refers to the distance between the lens and the image sensor when the lens is focused on infinity. It's typically measured in millimeters (mm) and is a key determinant of a lens's angle of view — the extent of the scene captured by the lens — and its magnification.

where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.