Question

GP Submarine A travels horizontally at 11.0 m/s through ocean water. It emits a sonar signal of frequency f = 5.27× 10³Hz in the forward direction. Submarine B is in front of submarine A and traveling at 3.00 m/s relative to the water in the same direction as submarine A. A crewman in submarine B uses his equipment to detect the sound waves ("pings") from submarine A. We wish to determine what is heard by the crewman in submarine B. (a) An observer on which submarine detects a frequency f' as described by Equation 17.19 ?

Answer 1

The frequency $5.3 \cdot 10^3 \mathrm{~Hz}$  that the submarine detects a frequency f' as described by Equation 17.19.

Explanation :

(a) Using the Doppler Shift formula, we can determine the frequency of the sonar signal that the crewman in submarine B heard:

$\begin{gathered}f_o=f_s\left(\frac{v-v_o}{v-v_s}\right), \\f_o=5.27 \cdot 10^3 \mathrm{~Hz} \cdot\left(\frac{1533 \frac{\mathrm{m}}{\mathrm{s}}-3 \frac{\mathrm{m}}{\mathrm{s}}}{1533 \frac{\mathrm{m}}{\mathrm{s}}-11 \frac{\mathrm{m}}{\mathrm{s}}}\right)=5.3 \cdot 10^3 \mathrm{~Hz} .\end{gathered}$

Hence, the frequecy of $5.3 \cdot 10^3 \mathrm{~Hz}$ that the submarine detects a frequency f' as described by Equation 17.19.

What do you mean by Frequency?

A frequency is the quantity of waves produced each second.

A measure of frequency is the number of times in a second that an alternating current (AC) changes from positive to negative. Direct currents do not experience this switching (DC). Hertz is used to measure frequency (Hz) The period is the length of time it takes for an AC current to start at zero, change from positive to negative, and then return to zero (i.e., the length of time it takes to complete one cycle), while the frequency is the reciprocal of the period. In contrast to low frequency, which has fewer waves per second but a longer period, high frequency refers to the number of waves per second and the length of the period.

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