Answer
434.1k+ views
Hint:In this solution, we are going to use the difference in two frequencies to find the frequency of beats. Both the frequencies are given in question, we just need to find their difference.
Complete Step by Step Answer:Given:
Frequency of the tuning fork ${f_1} = 250$Hz
Frequency of the piano key played ${f_2} = 200$Hz
The frequency of beats$f$that the piano tuner hears is nothing but the difference of the frequencies of the two waves that are interfering to produce the Beats. In this question, the two waves are of tuning fork and piano key.
The formula to find the frequency of beats$f$is given as:
The frequency of beats$f = \left| {{f_1} - {f_2}} \right|\;\;\;...........(1)$
Substituting the value of${f_1} = 250$Hz and ${f_2} = 200$Hz in equation (1), we get,
$\begin{array}{c}
f = \left| {250\;{\rm{Hz}} - 200\;{\rm{Hz}}} \right|\\
= 50\;{\rm{Hz}}
\end{array}$
Therefore, the frequency of beats is $50$Hz. So option (d) is our correct option.
Additional Information: A piano tuner uses the interesting phenomenon of Beats to tune his piano using a tuning fork. The tuner produces the sound of tuning fork and piano at the same time, and the two sounds are heard distinctively, we call it beats. The tuner then changes the tension of piano strings such that the beats frequency becomes zero, and one common sound must be heard when the tuning fork and the piano are played together.
Note: The modulus (two vertical bars) in the formula of frequency of the beats represent that the difference of the two frequencies of the interfering notes will always be positive (as frequency can never be negative). So, be aware that you can calculate the difference of frequencies as $\left( {{f_1} - {f_2}} \right)$ or$\left( {{f_2} - {f_1}} \right)$ but the resulting frequency of the beats must always be given with a positive sign.
Complete Step by Step Answer:Given:
Frequency of the tuning fork ${f_1} = 250$Hz
Frequency of the piano key played ${f_2} = 200$Hz
The frequency of beats$f$that the piano tuner hears is nothing but the difference of the frequencies of the two waves that are interfering to produce the Beats. In this question, the two waves are of tuning fork and piano key.
The formula to find the frequency of beats$f$is given as:
The frequency of beats$f = \left| {{f_1} - {f_2}} \right|\;\;\;...........(1)$
Substituting the value of${f_1} = 250$Hz and ${f_2} = 200$Hz in equation (1), we get,
$\begin{array}{c}
f = \left| {250\;{\rm{Hz}} - 200\;{\rm{Hz}}} \right|\\
= 50\;{\rm{Hz}}
\end{array}$
Therefore, the frequency of beats is $50$Hz. So option (d) is our correct option.
Additional Information: A piano tuner uses the interesting phenomenon of Beats to tune his piano using a tuning fork. The tuner produces the sound of tuning fork and piano at the same time, and the two sounds are heard distinctively, we call it beats. The tuner then changes the tension of piano strings such that the beats frequency becomes zero, and one common sound must be heard when the tuning fork and the piano are played together.
Note: The modulus (two vertical bars) in the formula of frequency of the beats represent that the difference of the two frequencies of the interfering notes will always be positive (as frequency can never be negative). So, be aware that you can calculate the difference of frequencies as $\left( {{f_1} - {f_2}} \right)$ or$\left( {{f_2} - {f_1}} \right)$ but the resulting frequency of the beats must always be given with a positive sign.
Recently Updated Pages
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of friction in our daily life
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)