Problem 3: Two sound waves traveling through water at the same speed. If a wave whose frequency is 3 MHz has a wavelength of 100 m, then find the wavelength of the wave whose frequency is 4.5 kHz.

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The crest is the highest point of the wave, whereas the lowest point of the wave is the trough. As the wavelength is a distance or length between two points, it is measured in meters, centimeters, millimeters, micrometers, Angstroms, etc. It is denoted by the Greek symbol Lambda ‘λ’.

Problem 2: A light wave is traveling in a vacuum. What will be the new wavelength of the wave if the new frequency of the wave is one-fifth of its old frequency?

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The wavelength of a wave decreases when its frequency increases, and vice versa. This inverse relationship is mathematically expressed as:

Let’s consider a thread that is tied to an end. Now hold the other end of the rope and oscillate it faster, resulting in higher frequency waves. We can also observe that the waves are produced with a shorter wavelength. Hence, we can draw the conclusion that there is a relationship between wavelength and frequency.

Problem 6: Two sound notes produced by a tuning fork are traveling at the same speed. If a wave whose frequency is 6 kHz has a wavelength of 100 mm, then find the wavelength of the wave whose frequency is 5.4 kHz.

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From the equation of the wavelength, we can tell that the wavelength of a wave is inversely proportional to its frequency, i.e., as the frequency of a wave increases, its wavelength decreases. Similarly, as the frequency of a wave decreases, its wavelength increases.

For example, let’s consider a wave whose new frequency is two times its old frequency. Now, what will be the new wavelength of the wave?

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Frequency is measured in terms of Hertz (Hz) or s-1. For humans, the audible range of sound frequencies is from 20 Hz to 20 kHz. Human ears cannot hear ultrasonic sounds, i.e., the frequencies above the audible range, and also infrasound, i.e., the frequencies less than the audible range.

Problem 5: A light wave is traveling in a vacuum. What will be the new frequency of the wave if the new wavelength of the wave is four times its old wavelength?

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Problem 1: Two sound waves are traveling through the air at the same speed. If a wave whose frequency is 45 kHz has a wavelength of 7.5 mm, then find the frequency of the wave whose wavelength is 100 nm.

As the frequency increases, the distance between consecutive wave crests or troughs decreases. As the frequency decreases, the distance between consecutive wave crests or troughs increases. The wavelength of a wave is inversely proportional to the frequency of the wave.

Wavelength of a wave decreases when frequency increases and the wavelength of a wave increases when frequency decreases.

Problem 7: If the new frequency of an electromagnetic wave is two-thirds of its old frequency, then what will be the new wavelength of the wave?

Problem 4: A light wave is traveling in a vacuum. What will be the new wavelength of the wave if the new frequency of the wave is three times its old frequency?