When a guitar string is sounded against a 440Hz note, 12 beats are heard in 2.0s.
a) what are the possible frequencies of the string?
b) when the same string is sounded against a 435Hz note, 33 beats are heard in 3.0s. What is the frequency of the string?
I honestly am very lost, I don't know how to solve these questions. Your help would be appreciated, thank you!
the "beats" are the frequency differences
a) 440 Hz ± (12/2) Hz
b) 435 Hz ± (33/3) Hz
which frequency is in both possibilities?
I can definitely help you solve these questions! Let's break them down step by step.
a) To find the possible frequencies of the string, we need to use the concept of beats. When two frequencies are close to each other, you can hear a pulsation or beating sound. The number of beats you hear in a certain amount of time can help determine the difference in frequency between the two sources.
In this case, we are given that when the guitar string is sounded against a 440Hz note, 12 beats are heard in 2.0s. We need to find the possible frequencies of the string.
To start, we know that the frequency of the note is 440Hz. Let's call the frequency of the guitar string f.
The number of beats (B) we hear is given as 12, and the time period (T) is given as 2.0s. The formula to calculate the difference in frequency between the two sources is:
Δf = B / T
Plugging in the values we have, we get:
Δf = 12 / 2.0
Simplifying the equation, we find that Δf = 6 Hz.
Now, to find the possible frequencies of the string, we need to consider both the higher and lower frequencies.
The higher frequency will be: f_high = 440 + Δf = 440 + 6 = 446 Hz.
The lower frequency will be: f_low = 440 - Δf = 440 - 6 = 434 Hz.
Therefore, the possible frequencies of the string are between 434 Hz and 446 Hz.
b) In the second question, we are told that when the same string is sounded against a 435Hz note, 33 beats are heard in 3.0s. We need to find the frequency of the string.
Similar to the previous question, let's call the frequency of the string f.
The number of beats (B) we hear is given as 33, and the time period (T) is given as 3.0s. We will use the same formula as before:
Δf = B / T
Plugging in the values we have, we get:
Δf = 33 / 3.0
Simplifying the equation, we find that Δf = 11 Hz.
Now, to find the frequency of the string, we need to know the frequency of the note it is compared to. In this case, it is 435Hz.
The frequency of the string will be: f = 435 + Δf = 435 + 11 = 446 Hz.
Therefore, the frequency of the string is 446 Hz.
I hope this helps! Let me know if you have any further questions.