Question

A bicycle wheel spins 25 times in 5 seconds. Calculate frequency of the wheel.
A. 15Hz
B. 10Hz
C. 40Hz
D. 5Hz

Answer 1

Frequency is the ratio of number of occurrences of a repeating event per unit time. Here, the bicycle wheel is spinning repeatedly 25 times in 5 seconds. Divide the no. of spins by the total time to calculate the frequency.

Complete step by step answer:
We are given that a bicycle wheel spins 25 times in 5 seconds.
We have to calculate the frequency of the wheel.
Frequency refers to the number of occurrences of an event per unit time.
Frequency is measured in cycles/second and can also be measured in Hertz (Hz).
$f = \dfrac{{no.of cycles}}{{time}}$
Total no. of cycles is 25
Total time taken is 5 seconds
$f = \dfrac{{25}}{5} \\\ \therefore f = 5 \\\$
The frequency is 5 cycles/second or 5 Hertz (5Hz).

So, the correct answer is “Option D”.

Additional Information:
Frequency is used in science and engineering to calculate the rate of oscillatory and vibratory motions such as radio waves, sound waves, mechanical vibrations etc. Police radios also use frequency.

Note:
Alternative approach for the above question.
Frequency is the reciprocal of time period, which means as the frequency of the wave increases, the time period decreases.
Frequency is inversely proportional to Time Period.
Time period is the time taken for one complete cycle to pass through a point.
It is the ratio of total time taken and total number of cycles it finishes in this time.
$t = \dfrac{{time}}{{no.of cycles}}$
Total time given is 5 seconds and the total number of cycles is 25.
$t = \dfrac{5}{{25}} \\\ \implies t = \dfrac{1}{5} \\\ \implies t = 0.2\sec /cycle \\\$
Frequency will be
$f = \dfrac{1}{t} \\\ t = 0.2\sec /cycles \\\ f = \dfrac{1}{{0.2}} \\\ \implies f = \dfrac{{10}}{2} \\\ \implies f = 5cycles/\sec \\\ \therefore f = 5Hz \\\$
The frequency of the bicycle wheel which spins 25 times in 5 seconds is 5 Hertz.