wavelength in water, steel, and brass

Question

When a sound wave is transferred from one medium to another, its frequency does not change. If the wavelength of a disturbance is 17cm in air, find its wavelength in water, steel, and brass if the speed of sound in water is 1450m/s, in steel 5000m/s, in brass 3500m/s, and in air 340 m/s.

Answer 1

The key to this is the relation among wavelength, frequency and speed.  Specifically:

 

wavelength * frequency = speed

 

So use the wavelength and speed in air to determine the frequency of this particular sound wave:

 

17 cm * ν = 340 m/s, where ν is the frequency.

 

So ν =20 per second

 

Now use this to find the wavelength in the other substances.  Let's use λ represent the wavelength

 

WATER:  λ * 20 per second = 1450 m/s

STEEL:  λ * 20 per second = 5000 m/s

BRASS:  λ * 20 per second = 3500 m/s

 

Solve each of these equations for λ to get the answers.