(a) 0.017 m - 17.2 m
The wavelength of a sound wave is given by
[tex]\lambda=\frac{v}{f}[/tex]
where
v = 343 m/s is the sound speed in air
f is the frequency
For the wave of frequency f = 20 Hz, we have
[tex]\lambda=\frac{343 m/s}{20 Hz}=17.2 m[/tex]
while for the wave of frequency f = 20,000 Hz, we have
[tex]\lambda=\frac{343 m/s}{20,000 Hz}=0.017 m[/tex]
So, the range of wavelength is
0.017 m - 17.2 m
(b) [tex]4.0 \cdot 10^{14} Hz-7.9 \cdot 10^{14} Hz[/tex]
The frequency of an electromagnetic wave is given by
[tex]f=\frac{c}{\lambda}[/tex]
where
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light
[tex]\lambda[/tex] is the wavelength
For the visible light with wavelength [tex]\lambda=380 nm=3.8\cdot 10^{-7} m[/tex], the frequency is
[tex]f=\frac{3\cdot 10^8 m/s}{3.8\cdot 10^{-7} m}=7.9 \cdot 10^{14} Hz[/tex]
For the visible light with wavelength [tex]\lambda=750 nm=7.5\cdot 10^{-7} m[/tex], the frequency is
[tex]f=\frac{3\cdot 10^8 m/s}{7.5\cdot 10^{-7} m}=4.0 \cdot 10^{14} Hz[/tex]
So, the range in frequencies is
[tex]4.0 \cdot 10^{14} Hz-7.9 \cdot 10^{14} Hz[/tex]
(c) 0.015 m
As said in part (a), the wavelength of a sound wave is given by
[tex]\lambda=\frac{v}{f}[/tex]
where
v = 343 m/s is the sound speed in air
f is the frequency
For the wave in this problem,
[tex]f=23 kHz = 23,000 Hz[/tex]
so the wavelength is
[tex]\lambda=\frac{343 m/s}{23,000 Hz}=0.015 m[/tex]
(d) 0.064 m
In solid, the speed of sound is
[tex]v=1480 m/s[/tex]
This means that if we use the formula to find the wavelength of the wave
[tex]\lambda=\frac{v}{f}[/tex]
we should now use v=1480 m/s.
Since the frequency of the wave is f = 23,000 Hz, the wavelength in the body is:
[tex]\lambda=\frac{1480 m/s}{23,000 Hz}=0.064 m[/tex]
