1) The length of the lead is 1700 m
2) The frequency of the wave is 400 Hz
Explanation:
1)
The wave in this problem is a sound wave, which is produced by the vibrations of the particles of air. It is a type of longitudinal wave (which means that the vibrations occur back-and-forth along the direction of propagation of the wave).
The speed of a sound wave in air is approximately
v = 340 m/s
In this problem, the sound wave is heard after a time of
t = 5 s
after the shot. Therefore, the distance travelled by the wave in this time (and therefore, the length of the lead) is
[tex]d=vt=(340)(5)=1700 m[/tex]
2)
The frequency of a wave is the number of complete cycles made by the wave in one second.
For the wave in this problem, we are told that the wave has 2000 whole wavelengths in 5 seconds: this means that the wave completes 2000 cycles in 5 seconds. Therefore, we can find the frequency by setting up the following proportion:
[tex]\frac{2000}{5}=\frac{x}{1}[/tex]
where x is the number of cycles made in 1 second. Solving for x,
[tex]x=\frac{2000\cdot 1}{5}=400 s^{-1}[/tex]
Therefore, the frequency of the wave is
[tex]f=400 Hz[/tex]
Learn more about waves and frequency:
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