Answer
Verified
442.5k+ views
Hint:-Frequency of the sound produced by flute is given by $n\dfrac{v}{{2l}}$ where $n$ is the harmonic number, $v$ is the speed of the wave and $l$ is the length of the flute.
Use the Doppler effect to find the apparent change in the frequency of sound due to the relative motion between the source of the sound (musician) and the observer (the person).
Complete step-by-step solution:-
Let us first know about harmonic
A harmonic number is basically an increasing series of sound components that can be heard above the audible fundamental frequency.
Frequency of the sound produced by flute is given by $n\dfrac{v}{{2l}}$ where $n$ is the harmonic number, $v$ is the speed of the wave and $l$ is the length of the flute.
So, as given in the question that the flute produces second harmonic sound waves, so $n = 2$
Also, the wave speed $v = 330m/s$ and length of the flute $l = 50cm = 0.5m$
Therefore, Frequency of the sound produced by flute
$f = \dfrac{{2 \times 330}}{{2 \times 0.5}} = 660Hz$
As given in the question velocity of observer, ${v_o} = 10km/hr = \dfrac{{25}}{9}m/s$
Now, we use the Doppler effect to find the apparent change in the frequency of sound heard by the observer due to the relative motion between the source (musician) and the observer (the person).
As the person runs towards the musician, so the frequency detected by observer, $f' = \left[ {\dfrac{{v + {v_o}}}{v}} \right]$
On substituting the values we have
$f' = \left[ {\dfrac{{\dfrac{{25}}{9} + 330}}{{330}}} \right]660 = 335.56 \times 2 \approx 666Hz$
Hence, option D is correct.
Note:- As we increase the frequency harmonics that can be heard above the fundamental frequency will cover up the harmonic spectrum of the sound. Harmonics can be difficult to differentiate among themselves as single components, nevertheless, they are there.
The Doppler effect is used to measure the velocity of detected objects in some types of radar. A beam of sound is fired from the radar at a moving target like a car or plane. For instance, a police can use a radar to detect speed of a motorist as it approaches or recedes from the radar source.
Use the Doppler effect to find the apparent change in the frequency of sound due to the relative motion between the source of the sound (musician) and the observer (the person).
Complete step-by-step solution:-
Let us first know about harmonic
A harmonic number is basically an increasing series of sound components that can be heard above the audible fundamental frequency.
Frequency of the sound produced by flute is given by $n\dfrac{v}{{2l}}$ where $n$ is the harmonic number, $v$ is the speed of the wave and $l$ is the length of the flute.
So, as given in the question that the flute produces second harmonic sound waves, so $n = 2$
Also, the wave speed $v = 330m/s$ and length of the flute $l = 50cm = 0.5m$
Therefore, Frequency of the sound produced by flute
$f = \dfrac{{2 \times 330}}{{2 \times 0.5}} = 660Hz$
As given in the question velocity of observer, ${v_o} = 10km/hr = \dfrac{{25}}{9}m/s$
Now, we use the Doppler effect to find the apparent change in the frequency of sound heard by the observer due to the relative motion between the source (musician) and the observer (the person).
As the person runs towards the musician, so the frequency detected by observer, $f' = \left[ {\dfrac{{v + {v_o}}}{v}} \right]$
On substituting the values we have
$f' = \left[ {\dfrac{{\dfrac{{25}}{9} + 330}}{{330}}} \right]660 = 335.56 \times 2 \approx 666Hz$
Hence, option D is correct.
Note:- As we increase the frequency harmonics that can be heard above the fundamental frequency will cover up the harmonic spectrum of the sound. Harmonics can be difficult to differentiate among themselves as single components, nevertheless, they are there.
The Doppler effect is used to measure the velocity of detected objects in some types of radar. A beam of sound is fired from the radar at a moving target like a car or plane. For instance, a police can use a radar to detect speed of a motorist as it approaches or recedes from the radar source.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE