Frequency can be defined as the ratio between the speed of the wave and its wavelength, that is
[tex]f= \frac{v}{\lambda}[/tex]
At the same time, the frequency is the inverse of the Period so
[tex]T = \frac{1}{f}[/tex]
If we join the two expressions we will have to
[tex]T = \frac{\lambda}{v}[/tex]
Replacing we have that
[tex]T = \frac{4.9*10^{-2}}{1522}[/tex]
[tex]T = 3.219*10^{-5} s[/tex]
Therefore the period of the wave is [tex] 3.219*10^{-5} s[/tex]
The period of the sound wave emitted from the porpoise is 3.22 × 10⁻⁵ seconds.
Given the data in the question;
Period; [tex]T = \ ?[/tex]
Period is simply time taken for one cycle to complete. It is expressed as:
[tex]T = \frac{1}{f}[/tex]
Where f is frequency.
So we find the frequency of the sound wave, using the expression for the relations between wavelength, frequency and speed of wave.
[tex]\lambda = \frac{v}{f}[/tex]
Where [tex]\lambda[/tex] is wavelength, f is frequency and v is speed.
We substitute our given values into the equation and find frequency
[tex]0.049m = \frac{1522m/s}{f}\\\\f = \frac{1522m/s}{0.049m }\\\\f = 31061.22s^{-1}[/tex]
Now, we find the Period
[tex]T = \frac{1}{f}\\\\T = \frac{1}{31061.22s^{-1}} \\\\T = 3.22*10^{-5}s[/tex]
Therefore, the period of the sound wave emitted from the porpoise is 3.22 × 10⁻⁵ seconds.
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