You have a tuning fork of unknown frequency. When you ring it alongside a tuning fork with known frequency of 360 Hz, you hear beats at a frequency of 10 Hz. When you ring it alongside a tuning fork with known frequency of 347 Hz, you hear beats at a frequency of 3 Hz. What is the unknown frequency?

Question

You have a tuning fork of unknown frequency. When you ring it alongside a tuning fork with known frequency of 360 Hz, you hear beats at a frequency of 10 Hz. When you ring it alongside a tuning fork with known frequency of 347 Hz, you hear beats at a frequency of 3 Hz. What is the unknown frequency?

Answer 1

You hear the difference so

1. could be 370 or 350

2. could be 350 or 344

so it is 350

Answer 2

You better google "beat frequency" !

Answer 3

To determine the unknown frequency of the tuning fork, we can use the concept of beat frequency.

The beat frequency is given by the absolute difference between the frequencies of the two tuning forks. Let's denote the unknown frequency of the tuning fork as "x".

From the given information:

When the unknown tuning fork is rung alongside the tuning fork with a known frequency of 360 Hz, the beat frequency is 10 Hz.

|360 Hz - x Hz| = 10 Hz ---- (Equation 1)

When the unknown tuning fork is rung alongside the tuning fork with a known frequency of 347 Hz, the beat frequency is 3 Hz.

|347 Hz - x Hz| = 3 Hz ---- (Equation 2)

We need to solve these two equations simultaneously to find the value of "x".

Let's first consider Equation 1:

|360 Hz - x Hz| = 10 Hz

This equation has two possible scenarios:

1. If 360 Hz - x Hz > 0:
360 Hz - x Hz = 10 Hz
360 Hz - 10 Hz = x Hz
x Hz = 350 Hz

2. If 360 Hz - x Hz < 0:
-(360 Hz - x Hz) = 10 Hz
x Hz - 360 Hz = 10 Hz
x Hz = 370 Hz

Next, let's consider Equation 2:

|347 Hz - x Hz| = 3 Hz

This equation also has two possible scenarios:

1. If 347 Hz - x Hz > 0:
347 Hz - x Hz = 3 Hz
347 Hz - 3 Hz = x Hz
x Hz = 344 Hz

2. If 347 Hz - x Hz < 0:
-(347 Hz - x Hz) = 3 Hz
x Hz - 347 Hz = 3 Hz
x Hz = 350 Hz

Since we have two possible values for "x" (350 Hz and 344 Hz), we need further information to determine the exact value.

Please provide additional details if available.

Answer 4

To determine the unknown frequency of the tuning fork, we can use the concept of beats. Beats occur when two tones with slightly different frequencies are played together, resulting in a periodic variation in amplitude, or a pulsation. The beat frequency is equal to the difference in frequencies between the two tones being played.

Let's analyze the information given:

1. When the unknown tuning fork is sounded alongside the 360 Hz tuning fork, we hear beats at a frequency of 10 Hz.
2. When the unknown tuning fork is sounded alongside the 347 Hz tuning fork, we hear beats at a frequency of 3 Hz.

To find the unknown frequency, we will set up two equations:

Equation 1: Unknown Frequency - 360 Hz = 10 Hz (from the first scenario)
Equation 2: Unknown Frequency - 347 Hz = 3 Hz (from the second scenario)

Now, let's solve these equations to find the value of the unknown frequency:

Equation 1: Unknown Frequency = 360 Hz + 10 Hz = 370 Hz
Equation 2: Unknown Frequency = 347 Hz + 3 Hz = 350 Hz

Now, we have two possible values for the unknown frequency: 370 Hz and 350 Hz. However, typically in this context, the tuning fork frequencies are assumed to be positive.

Therefore, the unknown frequency of the tuning fork is 370 Hz.