Answer
given,
temperature of wave propagates = 27°C
frequency of the sound wave = 4 kHz
speed of the sound wave depends upon the temperature according to the following equation
a) [tex]v = 331 \times \sqrt{1 + \dfrac{T_c}{273^0C}}[/tex]
at 27°C
[tex]v = 331 \times \sqrt{1 + \dfrac{27}{273^0C}}[/tex]
v = 347 m/s
at 0°C
[tex]v = 331 \times \sqrt{1 + \dfrac{0}{273^0C}}[/tex]
v = 331 m/s
velocity of the wave is decreased by 16 m/s or
velocity is decreased by 4.6 %
b) frequency of the wave will remain unchanged.
c) wavelength of the wave will also decrease by 4.6 %
[tex]\lambda = \dfrac{v}{f}[/tex]
[tex]\lambda = \dfrac{347}{4000}[/tex]
[tex]\lambda =86.7mm[/tex]
[tex]\lambda = \dfrac{v}{f}[/tex]
[tex]\lambda = \dfrac{331}{4000}[/tex]
[tex]\lambda =82.7mm[/tex]
