Questions: A stereo speaker produces a pure "G" tone, with a frequency of 392 Hz. What is the period T of the sound wave produced by the speaker? T= s What is the wavelength λwater of the same sound wave as it enters some water, where it has a speed of about 1480 m / s ? λwater= m What is the wavelength λair of this sound wave as it travels through air with a speed of about 341 m / s ? λair= m

A stereo speaker produces a pure "G" tone, with a frequency of 392 Hz.
What is the period T of the sound wave produced by the speaker?
T=
s

What is the wavelength λwater of the same sound wave as it enters some water, where it has a speed of about 1480 m / s ?
λwater=
m

What is the wavelength λair of this sound wave as it travels through air with a speed of about 341 m / s ?
λair=
m

Transcript text: A stereo speaker produces a pure "G" tone, with a frequency of 392 Hz. What is the period $T$ of the sound wave produced by the speaker? $T=$ $\square$ $s$ What is the wavelength $\lambda_{\text {water }}$ of the same sound wave as it enters some water, where it has a speed of about $1480 \mathrm{~m} / \mathrm{s}$ ? \[ \lambda_{\text {water }}= \] $\square$ m What is the wavelength $\lambda_{\text {air }}$ of this sound wave as it travels through air with a speed of about $341 \mathrm{~m} / \mathrm{s}$ ? \[ \lambda_{\text {air }}= \] $\square$ m

Solution

Solution Steps

Step 1: Calculate the Period $ T $ of the Sound Wave

The period $ T $ of a sound wave is the reciprocal of its frequency $ f $. Given the frequency $ f = 392 $ Hz, we can calculate the period using the formula: \[ T = \frac{1}{f} \] Substituting the given frequency: \[ T = \frac{1}{392} \approx 0.0026 \text{ s} \]

Step 2: Calculate the Wavelength $ \lambda_{\text{water}} $ in Water

The wavelength $ \lambda $ of a sound wave is given by the formula: \[ \lambda = \frac{v}{f} \] where $ v $ is the speed of sound in the medium and $ f $ is the frequency. For water, $ v = 1480 $ m/s and $ f = 392 $ Hz. Substituting these values: \[ \lambda_{\text{water}} = \frac{1480}{392} \approx 3.7755 \text{ m} \]

Step 3: Calculate the Wavelength $ \lambda_{\text{air}} $ in Air

Using the same formula for wavelength, but with the speed of sound in air $ v = 341 $ m/s: \[ \lambda_{\text{air}} = \frac{341}{392} \approx 0.8699 \text{ m} \]