Sound wave calculations

Question 1

What happens when a sound wave moves from one material to another?

Answer 1

• wave speed/velocity may change
• wavelength may change
• frequency will not change

wave speed = frequency x wavelength

Question 2

How are wavelength and wave speed related?

Answer 2

wavelength, λ , is directly proportional to wave speed, v

if the speed/velocity changes, the wavelength also changes
(e.g. a faster speed means longer/increased wavelengths
frequency is the number of waves produced per second, so does not change)

Question 3

What does the speed of sound depend on?

Answer 3

density of the material

a denser material increases the speed
the wave can be passed more easily from particle to particle in a dense material

solids are usually denser than liquids, which are denser than gas

(e.g. the speed of sound in water is 1500m/s, compared to air which is 330m/s)

Question 4

speed of sound in water and air

Answer 4

1500m/s

330m/s

Question 5

A wave of frequency 400Hz has a wavelength of 0.8m.

a) Calculate the speed of the wavelength is m/s [3]
b) Calculate its speed when it enters a material where its wavelength increases to 2.5m [3]

Answer 5

a) speed = f x λ
= 400 Hz x 0.8 m = 320m/s

b) wavelength increased from 0.8m to 2.5
frequency has stayed the same

v = 400 x 2.5 = 1000m/s

Question 6

Explain why sound waves travel at different speeds in different states of matter [3]

Answer 6

speed of sound is related to the density of the material

a greater density of material means the sound wave will travel through it faster

the particles will be more closely packed, allowing energy to be transferred between vibrating particles more easily

Question 7

Explain why sound waves do not travel through a vacuum [2]

Answer 7

sound waves are longitudinal waves that require a medium in which particles will vibrate to transfer the sound energy

a vacuum does not contain any particles, so these vibrations cannot occur in a vacuum, meaning the sound wave cannot travel through it

Question 8

a) The ratio of the wavelengths of a sound wave that has passed across the boundary between two materials is 2:5.
The speed of sound in the material of lower density is 342m/s.
Calculate the wave’s speed in the higher density. [2]

b) State the assumptions you have made [2]

Answer 8

a) speed of wave is directly related to the wavelength of speed, so speed in denser material = 342 x (5/2) = 855 m/s
(or (342/2) x 5 = 855 m/s

b) assumed that there is no change in frequency of the wave, and that the wave travels faster in the material of higher density