Physics notes – Sound
Free download and print from www.itute.com ©Copyright 2009 itute.com In the study of sound, we learn about the source, the medium and the receiver. Sound energy is transmitted from the source to the receiver via the medium. An example of the source is a tuning fork. It provides sound of a single frequency f. If the arms of the tuning fork vibrate 261 times in a second, we say its frequency of vibration is 261 Hz and the produced sound (vibration of the molecules in air, the medium) has the same frequency. As the arms of the tuning fork vibrate, a series of high (compression) and low (rarefaction) pressure regions in the air (the medium) is generated and propagates outwards. This series of compressions and rarefactions constitutes a travelling sound wave in the air.

∆p at a latter time 0.1 0 Q x

Another way to describe the sound wave is to stand at a particular position (e.g. position Q) in front of the source and record the pressure variation as a function of time t. ∆p at a particular position

0

t (10-3 s)

The interval from one high (or low) to the next is called the period T of the sound wave. 1 The relationship between f and T is f = . T The speed of sound
Rarefactions Compressions

d to find the speed of sound, where d t (m) is the distance travelled by the sound and t (s) is the time taken. The unit for v is ms-1.
Use the usual formula v = Example The timekeeper at an athletics meeting is 100 m from the starter. The time lag between the timekeeper seeing the flash of the starter’s pistol and hearing the sound is 0.29 s. Determine the speed of sound.

Sound wave in terms of air pressure variation Air pressure p (Nm ) at a particular time 105.0 normal air pressure
-2

v=

d 100 = = 345 ms-1. t 0.29

0 ∆p (Nm-2) at a particular time

x (m)

Speed of sound in different media The speed of sound depends on temperature and the type of medium that it travels in. E.g. Air (20° C) Water (20° C) Iron (20° C) 344ms-1 1498ms-1 5120ms-1

i

0.1 0 x (m)

The relationship between speed v (ms-1) and temperature T (K) is The last graph shows the pressure variation of the medium (air) versus distance in front of the source at a particular time. The distance from one compression (or rarefaction) to the next is called a wavelength λ. It is a travelling wave. The pattern moves away from the source as time progresses.
Physics notes – Sound ©Copyright 2009 itute.com

v∝ T .
The wave equation A sound wave travels a distance of one wavelength in a time λ 1 interval of one period, ∴ v = , and since f = , ∴ v = fλ . T T The last equation is known as the wave equation.
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Longitudinal and transverse waves Depending on the direction of motion of the particles of the medium relative to the direction of propagation, a wave can be classified as longitudinal or transverse. It is a longitudinal wave when the particles of the medium oscillate parallel to the direction of propagation of the wave. If the oscillation is perpendicular to the direction of propagation, it is called a transverse wave.

I

I∝

1 r2

0
Sound waves in air and under water are longitudinal. In a solid, a sound wave can be either longitudinal or transverse.

r

Example 1 At 2.4 m away from a bell, the intensity is 9.0 × 10-4 Wm-2. What is the intensity at 7.2 m away? At 1.2 m away? 7.2 m is 3 times 2.4 m, ∴the intensity is

Sound intensity Sound intensity I measures the amount of sound energy E arriving at a particular surface of area A, over a time interval ∆t. E E P , and since power P = , ∴I = . It is defined as I = A∆t ∆t A The units are W or Js-1 for P, m2 for A, and Wm-2 or Js-1m-2 for I. Sound intensity is an objective measure. Anyone handling the measuring device correctly will record the same reading. The perceived loudness of the sound by a person is a subjective sensation. In general, the greater the intensity, the louder is the sound. But perceived