Physics

Physics

Problem

A factory siren emits a continuous sound wave whose wavelength in air at 20∘C20^{\circ}\text{C} is 50 cm50\,\text{cm}. a. (a) Taking the speed of sound in air as 343 m/s343\,\text{m/s}, calculate the frequency of the siren. b. (b) The same siren is attached to a research submarine. Under water, the speed of sound is 1530 m/s1530\,\text{m/s}. Keeping the frequency unchanged, calculate the wavelength of the sound in seawater. Express your answer in metres and in centimetres. c. (c) The submarine emits this sound pulse and receives its reflection from the seabed after 0.80 s0.80\,\text{s}. Calculate the depth of the sea at that location.
Intuitive explanation

The key is connecting wavelength to frequency using the wave equation v=fλv = f\lambda. Since the speed of sound in air at 20°C is a known constant ( 343 m/s), you can find the siren's frequency—which doesn't change as the sound travels. Once you have frequency, you can predict how the wavelength would shift in different conditions, like when the siren moves or the temperature changes.

Intuitive explanation

The key is connecting wavelength to frequency using the wave equation v=fλv = f\lambda. Since the speed of sound in air at 20°C is a known constant ( 343 m/s), you can find the siren's frequency—which doesn't change as the sound travels. Once you have frequency, you can predict how the wavelength would shift in different conditions, like when the siren moves or the temperature changes.

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