Question 306: Waves

Question

The frequency of two tuning forks A and B are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork C . When A and B are sounded together, 10 beats are produced in 1 second. The frequency of tuning fork C is

Accepted Answer

To determine the frequency of tuning fork C, let's denote its frequency as $ f $.
Tuning fork A has a frequency that is 1.4% more than tuning fork C. Therefore, the frequency of A, $ f_A $, is given by:
$$ f_A = f + 0.014f = 1.014f $$
Similarly, tuning fork B has a frequency that is 2.6% less than that of tuning fork C. Therefore, the frequency of B, $ f_B $, is given by:
$$ f_B = f - 0.026f = 0.974f $$
When tuning forks A and B are sounded together, they produce 10 beats per second, which implies that the absolute difference in their frequencies is 10 Hz:
$$ |f_A - f_B| = 10 $$
Substituting the expressions for $ f_A $ and $ f_B $:
$$ |1.014f - 0.974f| = 10 $$
This simplifies to:
$$ |0.04f| = 10 $$
Solving for $ f $:
$$ 0.04f = 10 \quad \Rightarrow \quad f = \frac{10}{0.04} = 250 $$
Thus, the frequency of tuning fork C is 250 Hz.
Option A: 250 Hz

Answer

250 Hz

Answer

300 Hz

Answer

340 Hz

Answer

400 Hz

Waves

The frequency of two tuning forks A and B are respectively 1.4 \% more and 2.6 \% less than that of the tuning fork C . When A and B are sounded together, 10 beats are produced in 1 second. The frequency of tuning fork C is

Choose the correct answer: