if three sources of sound of equal intensities and having frequencies 300 Hz , 301 Hz and 302 Hz are sounded together, the number of beats heard is

Options

A. 1
B. 2
C. 3
D. none of the above

Answer

To solve the problem of determining the number of beats heard when three sound sources of frequencies 300 Hz, 301 Hz, and 302 Hz are sounded together, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Beats**:
- When two sound waves of slightly different frequencies interfere, they produce a phenomenon called beats. The number of beats per second is equal to the absolute difference in their frequencies.

2. **Identify the Frequencies**:
- We have three frequencies:
- \( f_1 = 300 \, \text{Hz} \)
- \( f_2 = 301 \, \text{Hz} \)
- \( f_3 = 302 \, \text{Hz} \)

3. **Calculate the Beats Between Each Pair**:
- Calculate the beats between \( f_1 \) and \( f_2 \):
\[ |f_1 - f_2| = |300 - 301| = 1 \, \text{beat per second} \]
- Calculate the beats between \( f_2 \) and \( f_3 \):
\[ |f_2 - f_3| = |301 - 302| = 1 \, \text{beat per second} \]
- Calculate the beats between \( f_1 \) and \( f_3 \):
\[ |f_1 - f_3| = |300 - 302| = 2 \, \text{beats per second} \]

4. **Total Number of Distinct Beats**:
- The total number of distinct beats heard is determined by the maximum frequency difference.
- The pairs that produce beats are:
- \( f_1 \) and \( f_2 \) produce 1 beat.
- \( f_2 \) and \( f_3 \) produce 1 beat.
- \( f_1 \) and \( f_3 \) produce 2 beats.
- However, since the beats are periodic, we only consider the maximum frequency difference, which is 2 beats per second.

5. **Conclusion**:
- The total number of beats heard when these three frequencies are sounded together is:
\[ \text{Total Beats} = 2 \]

### Final Answer:
The number of beats heard is **2**.