Chapter 12, Problem 52P

To determine

To find: The frequency of emitting horns.

Answer to Problem 52P

  $f=120.26\text{ Hz}\text{.}$

Explanation of Solution

Given:

Beat frequency, $f_{beat}$ $=5.5\text{ Hz}.$

Speed of the vehicle (Source) $\left(v\right)$ $=15\text{ m/s}.$

Temperature $\left(T\right)$ $=20°\text{C}$

The speed at $T=20°\text{C}$ $=343\text{ m/s }\left(331+\left(0.6\times 20\right)\right)$

Formula used:

Write the expression of the frequency of horns.

  $f=f_{beat}\frac{v-v_{source}}{v_{source}}\text{ Hz}$ .

  $f$ = Frequency of horns, Hz

  $f_{beat}$ =beat frequency, Hz

  $v_{source}$ = speed of the vehicle (source), m/s

  $v$ = Ideal speed of wave = 343 m/s

Calculation:

From the Doppler effect formula is given as,

  $f=f_{beat}\frac{v-v_{source}}{v_{source}}\text{ Hz}$

By putting all the values from the above.

  $f=5.5\text{ Hz}\times \frac{343\text{ m/s}-15\text{ m/s}}{15\text{ m/s}}\text{ Hz}\text{.}$

  $f=120.26\text{ Hz}\text{.}$

Conclusion:

The frequency of horns that can emit 120.26 Hz frequency.