Question

Calculate the wavelengths in air at 20 ?C for sounds in the maximum range of human hearing, 20 Hz to 20000 Hz.

A.) ?(20 Hz), ?(20000 Hz) =

B.) What is the wavelength of a 55 MHz ultrasonic wave?

Answer 1

Part A(i).

Relation between wavelength and frequency is given by:

= V/f

V = Speed of sound at 20 C = 343 m/s

f = freuency = 20 Hz

So,

1 = 343/20

1 = 17.15 m = wavelength

In two significant figures:

1 = 17 m

Part A(ii)

when f = freuency = 20000 Hz

So,

2 = 343/20000

2 = 17.15*10^-3 m = wavelength

In two significant figures:

2 = 17*10^-3 m

Part B.

V = speed of ultrasonic wave = 343 m/s

So, frequency = 55 MHz = 55*10^6 Hz

wavelength = V/f = 343/(55*10^6)

wavelength = 6.236*10^-6 m

In two significant figures:

wavelength = 6.2*10^-6 m

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