Question

a second wave of lower frequency was emitted and interfered with the first. in t = 35 s, n1 = 78 beats were heard. what is an expression for the frequency (f2) of the second sound wave?

Answer 1

Final answer:

In the given scenario, the expression for the frequency (f2) of the second sound wave (lower frequency) is

�

2

=

�

1

�

f

2

​

=

t

n

1

​

​

, where

�

1

n

1

​

is the number of beats (78 beats) heard in time

�

=

35

t=35 seconds.

Step-by-step explanation:

In the context of interference between two sound waves, the frequency of the second wave (f2) can be determined using the formula

�

2

=

�

1

�

f

2

​

=

t

n

1

​

​

, where

�

1

n

1

​

represents the number of beats heard and

�

t is the time interval (35 seconds in this case). In the given problem,

�

1

n

1

​

is specified as 78 beats, and

�

t is given as 35 seconds.

To calculate the frequency (

�

2

f

2

​

), substitute the given values into the formula:

�

2

=

78

35

≈

2.228

beats/second

.

f

2

​

=

35

78

​

≈2.228 beats/second.

Therefore, the expression for the frequency (

�

2

f

2

​

) of the second sound wave is approximately

2.228

2.228 beats per second.

This formula signifies the rate at which the second wave's lower frequency interferes with the first wave. The number of beats (78) indicates the constructive or destructive interference between the two waves within the specified time interval (35 seconds).

Answer 2

The expression for the frequency of the second sound wave (f2) can be found using the equation for beat frequency: fB = |f1-f2|. In this case, fB is given as 78 beats in 35 seconds, so f2 = f1 - 78.

Step-by-step explanation:

The expression for the frequency of the second sound wave (f2) can be found using the equation for beat frequency:

fB = |f1-f2|

In this case, the beat frequency (fB) is given as 78 beats in 35 seconds. Since beat frequency is the difference between the frequencies of the two waves, we can set up the equation as:

78 = |f1-f2|

Since we know f1, the frequency of the first wave, and we want to find f2, the frequency of the second wave, we can rearrange the equation as:

f2 = f1 - 78

So, the expression for the frequency of the second sound wave is f2 = f1 - 78.