Question:
There are $26$ tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives $3$ beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?
There are $26$ tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives $3$ beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?
Updated On: Sep 15, 2024
- 100 Hz
- 99 Hz
- 96 Hz
- 103 Hz
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The Correct Option is B
Solution and Explanation
Each tuning forck gives 3 beats with the next, so the difference in the frequencies of two consecutive forks is 3 .
$\therefore f_{26} =f_{1}+(n-1) \times-3$
$f =2 f+(26-1) \times-3$
$f =75\, Hz .$
$\therefore$ Frequency of 18 th tuning fork
$f_{18} =f_{1}+(18-1) \times-3$
$=2 \times 75+17 \times-3$
$=150-51=99\, Hz$.
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Concepts Used:
Sound
Sound is a vibration that propagates the mechanical wave of displacement and pressure, through a medium can be of any matter. In other words, the sound is the thin line between Music sound and Noise.
Types of Sounds:
Sound can be divided into two types depending on its frequency. The following are:-
Infrasonic Waves:
- Infrasonic waves have a frequency lower than 20 Hz. Since it is below the human hearing range, it is inaudible to humans.
- However, several other living organisms use these waves to communicate, whales, sharks, elephants, hippopotamus, etc. these waves are also used in the scientific field, it is used to study upcoming earthquakes, volcanic eruptions, human heart rates, rock formation stages, etc.
Ultrasonic waves:
- Ultrasonic waves have a frequency higher than 20 kHz. Since it is above the human hearing range, it is inaudible to humans.
- These waves are used in the scientific field, it is used to study human heart rates, to take sonograms, navigation of directions, imaging things, uniform sample mixing, communication, testing of samples, etc.