You have a tuning fork of unknown frequency. When your ring it alongside tuning fork with frequency of 360Hz, you hear beats at frequency of 2 Hz. When you ring it alongside tuning fork with known frequency of 355Hz, you hear beats at a frequency of 3Hz. What is the unknown frequency?

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Thank you

What is 352?

360Hz + 2Hz= 362Hz

360Hz - 2Hz = 358Hz

355 + 3Hz= 358Hz
355 - 3Hz= 352Hz

Thus, 358Hz is the answer.

To find the unknown frequency, let's denote it as f.

Given:
Frequency of the first tuning fork = 360 Hz
Frequency of the second tuning fork = 355 Hz
Frequency of beats with the first tuning fork = 2 Hz
Frequency of beats with the second tuning fork = 3 Hz

When two frequencies are close to each other, the resulting beat frequency can be calculated using the formula:

Beat frequency = |f₁ - f₂|

From the given information, we can set up the two equations:

|f - 360| = 2 ---- (Equation 1)
|f - 355| = 3 ---- (Equation 2)

To solve these equations, we need to consider two possible cases:

Case 1: (f - 360) > 0 and (f - 355) > 0
In this case, the absolute values can be removed from the equations. We can rewrite Equations 1 and 2 as:

f - 360 = 2 ---- (Equation 3)
f - 355 = 3 ---- (Equation 4)

Solving equations 3 and 4 will give us the value of f for this case.

Case 2: (f - 360) < 0 and (f - 355) < 0
In this case, the absolute values can be removed from the equations, but the signs will be reversed. We can rewrite Equations 1 and 2 as:

-(f - 360) = 2 ---- (Equation 5)
-(f - 355) = 3 ---- (Equation 6)

Solving equations 5 and 6 will give us the value of f for this case.

Let's solve both cases:

Case 1:
f - 360 = 2
Adding 360 to both sides:
f = 2 + 360
f = 362 Hz

Case 2:
-(f - 360) = 2
Expanding the brackets:
-f + 360 = 2
Subtracting 360 from both sides:
-f = 2 - 360
-f = -358
Multiplying both sides by -1:
f = 358 Hz

Therefore, the unknown frequency of the tuning fork can be either 362 Hz or 358 Hz.

To solve this problem, we need to understand the concept of beats. In acoustics, beats are the periodic variations in sound intensity that occur when two sounds with slightly different frequencies are superimposed. The beat frequency is the difference between the frequencies of the two sources.

Let's assume the unknown frequency of the tuning fork is "f" Hz. When the unknown tuning fork is struck alongside the 360 Hz fork, we hear beats of 2 Hz. This means the beat frequency is the difference between the two frequencies:

Beat frequency = Frequency of known fork - Frequency of unknown fork
2 Hz = 360 Hz - f Hz

Similarly, when the unknown tuning fork is struck alongside the 355 Hz fork, we hear beats of 3 Hz:

3 Hz = 355 Hz - f Hz

Now we have a system of two equations, and we can solve them simultaneously using a method called substitution. Let's solve for "f" using these equations:

From the first equation: 2 Hz = 360 Hz - f Hz
f = 360 Hz - 2 Hz
f = 358 Hz

Now let's substitute this value of "f" into the second equation:

3 Hz = 355 Hz - f Hz
3 Hz = 355 Hz - 358 Hz
3 Hz = -3 Hz

Uh-oh! We've encountered a problem. The equation doesn't make sense, which means there is no valid frequency that satisfies both conditions. It seems there is an error in data or calculations, which needs to be reevaluated.

Please double-check the given frequencies and the calculations.