Beat FrequencyWhat is the new tension in the string that slipped?

[r_swayze]

Two identical strings are sounding the same fundamental tone of frequency 156 Hz. Each string is under 228 N of tension. The peg holding one string suddenly slips, reducing its tension slightly, and the two tones now create a beat frequency of three beats per second. What is the new tension in the string that slipped?

My attempt so far:

f_beat = f₁ - f₂ = 3Hz

f₁ = 156Hz

3Hz - 156Hz = -f₂

f₂ = 153Hz

So how do I find the tension for this frequency? Usually there is more information given such as the linear density or speed of the wave. I don't see how I can find the tension without those variables. Any help?

 

[rl.bhat]

For identical strings frequency f = k*(T)^1.2, where k is constant and T is the tension in the string. So
f1/f2 = (T1/T2)^1/2.
You have already found f1 and f2. T1 is given. Find T2.

 

[kerimek]

As a scientist, it is important to have all the necessary information to accurately solve a problem. In this case, the frequency and tension of the strings are given, but the linear density or speed of the wave is missing. Without this information, it is not possible to calculate the new tension in the string that slipped.

The linear density of a string refers to its mass per unit length, while the speed of a wave on a string depends on the tension and linear density of the string. Therefore, without knowing the linear density, we cannot accurately determine the new tension in the string.

It is also worth noting that the beat frequency is not directly related to the tension of the string but rather to the difference in frequency between the two strings. In this case, the beat frequency is 3Hz, but we cannot use this information to determine the new tension in the string that slipped.

In conclusion, without additional information, it is not possible to accurately determine the new tension in the string that slipped. As a scientist, it is important to have all the necessary data to accurately solve a problem and draw conclusions.