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The following sound waves have what velocity?

(a) \( f = 36.3 \, \text{Hz}, \, \lambda = 11.0 \, \text{m} \)

(b) \( f = 363.0 \, \text{Hz}, \, \lambda = 4.80 \, \text{m} \)

(c) \( f = 3,630.0 \, \text{Hz}, \, \lambda = 11.0 \, \text{cm} \)

(d) \( f = 36,300.0 \, \text{Hz}, \, \lambda = 4.80 \, \text{cm} \)

Answer :

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:

[tex]v = \lambda f[/tex] (1)

Where [tex]\lambda[/tex] 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

[tex]v = (11.0 m)(36.3 Hz)[/tex]

But 1 Hz = s⁻¹, therefore:

[tex]v = (11.0 m)(36.3 s^{-1})[/tex]

[tex]v = 399.3 m.s^{-1}[/tex]

[tex]v = 399.3 m/s[/tex]

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

(b) f = 363.0 Hz, λ = 4.80 m

[tex]v = (4.80 m)(363.0 Hz)[/tex]

[tex]v = (4.80 m)(363.0 s^{-1})[/tex]

[tex]v = 1742.4 m.s^{-1}[/tex]

[tex]v = 1742.4 m/s[/tex]

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 [tex]\lambda[/tex] in meters.

[tex]11.0 cm . \frac{1 m}{100 cm}[/tex] ⇒ [tex]0.11 m[/tex]

[tex]v = (0.11 m)(3630.0 Hz)[/tex]

[tex]v = (0.11 m)(3630.0 s^{-1})[/tex]

[tex]v = 399.3 m.s^{-1}[/tex]

[tex]v = 399.3 m/s[/tex]

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

(d) f = 36,300.0 Hz, λ = 4.80 cm

[tex]4.80 cm . \frac{1 m}{100 cm}[/tex] ⇒ [tex]0.048 m[/tex]

[tex]v = (0.048 m)(36300.0 Hz)[/tex]

[tex]v = (0.048 m)(36300.0 s^{-1})[/tex]

[tex]v = 1742.4 m.s^{-1}[/tex]

[tex]v = 1742.4 m/s[/tex]

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

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