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

Answer:

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

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.

$11.0 cm . \frac{1 m}{100 cm}$ ⇒ $0.11 m$

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

$v = (0.11 m)(3630.0 s^{-1})$

$v = 399.3 m.s^{-1}$

$v = 399.3 m/s$

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

(d) f = 36,300.0 Hz, λ = 4.80 cm

$4.80 cm . \frac{1 m}{100 cm}$ ⇒ $0.048 m$

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

$v = (0.048 m)(36300.0 s^{-1})$

$v = 1742.4 m.s^{-1}$

$v = 1742.4 m/s$

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