Question

The most soaring vocal melody is in Johann Sebastian Bach's Mass in B Minor. In one section, the basses, tenors, altos, and sopranos carry the melody from a low D to a high
A. In concert pitch, these notes are now assigned frequencies of 146.8Hz and 880.0 Hz . Find the wavelengths of(c) the initial note and

Answer 1

The wavelength of the initial note is 2.34m

What do you mean by the term wavelength?

The distance between two successive crests or troughs of a wave is known as its wavelength. It is measured in the wave's direction. The distance a wave travels between its crests or troughs is known as its wavelength (which may be an electromagnetic wave, a sound wave, or any other wave). The wave's crest is its highest point, while its dip is its lowest. Because a wavelength represents a distance or length, it is expressed in length units like meters, centimeters, millimeters, nanometers, etc. Light's wavelength changes with color, or it differs for each hue. While violet has the shortest wavelength, red has the longest.

wavelength = v/f

Given:

Initial frequency, $f_{initial} = 146.8 Hz$

Final frequency, $f_{final} = 880\;Hz$

Sound Level, $\beta = 79\;dB$

We know that,

Speed of the sound, $v=343\;m/s$

Density of air, $\rho=1.2\;kg/m^{3}$

Wavelength, $\lambda = \frac{v}{f}$

Wavelength of initial note is,

$\lambda = \frac{v}{f_{initial} }$

Substitute the known values in the above equation,

$\lambda = \frac{343}{146.8}$

$\lambda = 2.34\;m$

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