Question

The following sound waves have what velocity? (a) f = 36.3 Hz, λ = 11.0 m m/s (b) f = 363.0 Hz, λ = 4.80 m m/s (c) f = 3,630.0 Hz, λ = 11.0 cm m/s (d) f = 36,300.0 Hz, λ = 4.80 cm m/s

Answer 1

(a) v = 399.3 m/s, (b) v = 1742.4 m/s, (c) v = 399.3 m/s, (d) v = 1742.4 m/s

Step-by-step explanation:

The velocity of a wave can be defined as:

`v = \lambda f` (1)

Where
`\lambda` and f are the wavelength and frequency of the sound wave.

The values for each case will be replaced in equation (1).

(a) f = 36.3 Hz, λ = 11.0 m

`v = (11.0 m)(36.3 Hz)`

But 1 Hz = s⁻¹, therefore:

`v = (11.0 m)(36.3 s^(-1))`

`v = 399.3 m.s^(-1)`

`v = 399.3 m/s`

So the sound wave has a velocity of 399.3 m/s.

(b) f = 363.0 Hz, λ = 4.80 m

`v = (4.80 m)(363.0 Hz)`

`v = (4.80 m)(363.0 s^(-1))`

`v = 1742.4 m.s^(-1)`

`v = 1742.4 m/s`

So the sound wave has a velocity of 1742.4 m/s.

(c) f = 3,630.0 Hz, λ = 11.0 cm

Before using equation (1) it is necessary to express
`\lambda` in meters.

`11.0 cm . (1 m)/(100 cm)` ⇒
`0.11 m`

`v = (0.11 m)(3630.0 Hz)`

`v = (0.11 m)(3630.0 s^(-1))`

`v = 399.3 m.s^(-1)`

`v = 399.3 m/s`

So the sound wave has a velocity of 399.3 m/s.

(d) f = 36,300.0 Hz, λ = 4.80 cm

`4.80 cm . (1 m)/(100 cm)` ⇒
`0.048 m`

`v = (0.048 m)(36300.0 Hz)`

`v = (0.048 m)(36300.0 s^(-1))`

`v = 1742.4 m.s^(-1)`

`v = 1742.4 m/s`

So the sound wave has a velocity of 1742.4 m/s.