Physics

Problem

A train whistle produces a continuous sound whose time period is measured to be

0.004\,\text{s}

. a. (i) Show that the wavelength

\lambda

of any wave can be expressed in terms of its speed

v

and its time period

T

. b. (ii) At

15^{\circ}\text{C}

, the speed of sound in air is

340\,\text{m\!/s}

. Calculate the wavelength of the whistle’s sound in air at this temperature. c. (iii) The speed of sound increases by about

0.6\,\text{m\!/s}

for every

1^{\circ}\text{C}

rise in temperature. Determine the wavelength of the same sound at

30^{\circ}\text{C}

, assuming its frequency remains unchanged.

Intuitive explanation

The key here is connecting the physical measurement you can observe—how long one complete vibration takes—to the frequency of the sound wave. Period and frequency are reciprocals of each other, so if you know how long one cycle lasts, you can immediately find how many cycles happen per second. This frequency then tells you everything about the pitch and behavior of the sound wave.

Intuitive explanation

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