Chapter 1: Q1E (page 1)

15.1. The speed of sound in air at $20 ° C$ is 344m/s . (a) What is the wavelength of a sound wave with a frequency of 784 Hz , corresponding to the note 5G on a piano, and how many milliseconds does each vibration take? (b) What is the wavelength of a sound wave one octave higher (twice the frequency) than the note impart (a)?

Expert verified

The wavelength of a sound wave is 0.439 m and the time period it takes to complete its cycle 1.28 ms .

Step by step solution

The wavelength of the wave is given by_{$λ = \frac{v}{f}$}

Here, $λ$ is the wavelength of the wave, v is the speed of sound, f is the frequency

The period can be defined as the time taken required to complete one cycle or oscillation.

The time period of sound wave is given by $T = \frac{1}{f}$

Here, T is the time period of the wave.

Consider the given data as below.

The frequency, $f = 784 Hz$

The velocity, $v = 334 m / s$

Formula to calculate the wavelength of the wave is

_{$λ = \frac{v}{f}$}

Substitute 334 m/s for v and 784 Hz for f in the above equation.

_{$λ = \frac{334}{784} = 0.439 m$}

Therefore, the wavelength of a sound wave is 0.439 m.

Formula to calculate the time period of the wave

_{$T = \frac{1}{f} T = \frac{1}{784 Hz} = (0.001275 s) (\frac{10^{3} ms}{1 s}) = 1.28 ms$}

Therefore, the time period it takes to complete its cycle $1.28 ms$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.