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Chapter 1: Q1E (page 1)

15.1. The speed of sound in air at20掳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)?

Short Answer

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

01

Wavelength of the wave and the time period of sound wave.

The wavelength of the wave is given by位=vf

Here,位 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 byT=1f

Here, T is the time period of the wave.

02

To calculate the wavelength of the wave.

Consider the given data as below.

The frequency, f=784Hz

The velocity, v=334m/s

Formula to calculate the wavelength of the wave is

位=vf

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

位=334784=0.439m

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

03

To calculate the time period of the wave.

Formula to calculate the time period of the wave

T=1fT=1784Hz=0.001275s103ms1s=1.28ms

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

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