Question

A toothed wheel is rotating at 240 rpm and a postcard is held against the teeth. If the pitch of the tone is 256 Hz, then the number of teeth on the rotating wheel is
A) 256
B) 128
C) 64
D) 32

Answer 1

Hint: In toothed wheel it is a simple machine consisting of a circular frame with spokes (or a solid disc) that can rotate on a shaft or axle and frequency is equal to the product of rotation per second to the no. of teeth. We just change the rotation per minute into rotation per second and rest the things are given to solve the question.

Complete step by step answer:
A toothed wheel is essentially a wheel having on its periphery a number of projections at equal distances apart, with corresponding indentations or spaces into which the teeth of the corresponding teeth can fit with ease. The simplest form of a toothed wheel is evidently a wheelset on an.
Pitch, in speech, the relative highness or lowness of a tone as perceived by the ear, which depends on the number of vibrations per second produced by the vocal cords. Pitch is the main acoustic correlate of tone and intonation
Now coming to the question,
We are given that a toothed wheel is rotating at 240 rpm and a postcard is held against the teeth.
Given that the pitch of the tone is 256 Hz
Rotation at 240 rpm means $\dfrac{{240}}{{60}}$ rotation per second.
On solving it we will get 4 rotations per second.
Now, Frequency is equal to the product of rotation per second to the no. of teeth.
This implies $\nu $ =4×n where, $\nu $ denotes frequency
Then the number of teeth on the rotating wheel is n=$\dfrac{\nu }{4}$ ($\therefore \nu $ =256Hz)
Putting the values we will get the number of teeth equal to 64.

Hence, option C is correct.

Additional information:
Advantages of using a toothed wheel:
- Lubricant-free running
- Ideal sliding properties
- Excellent noise and damping characteristics
- Very good torque transmission
- Retains shape, even underwater
- Very low-maintenance, even in continual use

Usage to toothed wheel:
- Automotive.
- Storage & Conveying technology.
- Lifts & Cable railways.
- Petro chemistry.
- Printing industry.
- Medical engineering
- Packaging & Food industry.
- Paper & Fiber production.

Note:
These questions are simple and based on the formulas. One needs to remember to change the unit of the given rotations and not to change if it is given in seconds as this is the standard way to do it. Simple math is used in solving the question hence needs to be cautious before calculating.