Question

For production of beats the two sources must have

• A. different frequencies and same amplitude
• B. different frequencies
• C. different frequencies, same amplitude and same phase
• D. different frequencies and same phase

Answer 1

The Correct Option is B

The question asks about the conditions required for the production of beats by two sound sources. To understand this, let's break down the concept of beats:

1. The phenomenon of beats occurs when two sound waves of slightly different frequencies interfere with each other. This interference causes the amplitude of the resultant wave to vary with time, giving rise to the perception of periodic increases and decreases in loudness, known as beats. The frequency of the beats is equal to the absolute difference between the two frequencies.
2. The essential requirement for the production of beats is that the two sound waves must have different frequencies. The difference in frequencies causes the waves to alternately reinforce and cancel each other as they move in and out of phase, leading to the beats effect.
3. Other factors like amplitude and phase are not necessary for the formation of beats. However, for a prominent beat pattern, the amplitudes could be similar, but this is not a strict requirement.

Now, let’s analyze the options given:

1. different frequencies and same amplitude
   : While having the same amplitude might make the beats more noticeable, it's not necessary for their formation.
2. different frequencies
   : This is correct because the main criterion for beats is that the waves must have different frequencies.
3. different frequencies, same amplitude and same phase
   : Same amplitude and phase are not mandatory for beats to occur.
4. different frequencies and same phase
   : Like amplitude, having the same phase is also not required.

Therefore, the correct answer is different frequencies as it is the only essential condition for the production of beats.