Statement :- We assume the orthagonal sequence
in Hilbert space, now
, the Fourier coefficients are given by:

Then Bessel's inequality give us:

Proof :- We assume the following equation is true

So that,
is projection of
onto the surface by the first
of the
. For any event, 
Now, by Pythagoras theorem:


Now, we can deduce that from the above equation that;

For
, we have

Hence, Proved
Explanation:
The efficiency of a machine is 70% means 30% of the applied force is wasted in overcoming friction and 70% of the applied force is used to do the work
We assume that horn releases sound of constant frequency. In order for observer to observe different frequency either horn or observer or both must move.
This happens due to Doppler effect. It states that when position of source of sound and observer relative to each other changes, the observed frequency also changes. If the source emits sound of constant frequency than observed frequency will be either higher or lower than original.
When distance between source and observer increases the observed frequency will be lower. This is because same number of sound waves must cover greater distance so they have greater wavelength.
When distance between source and observer decreases the observed frequency will be higher. This is because same number of sound waves must cover smaller distance so they have smaller wavelength.
Wavelength and frequency are inversely proportional meaning when one increases the other drecreases.
From this explanation we can find answer for our question. <span>If we wanted the pitch of a horn to drop relative to an observer we need to move horn away from an observer.</span>
Answer:
Longitudinal waves have the same direction of vibration as their direction of travel. This means that the movement of the medium is in the same direction as the motion of the wave.