Two loudspeakers $L_1$ and $L_2$,driven by a common oscillator and amplifier,are arranged as shown. The frequency of the oscillator is gradually increased from zero,and the detector at $D$ records a series of maxima and minima. If the speed of sound is $330 \, m/s$,then the frequency at which the first maximum is observed is .... $Hz$.

Two waves represented by $y_1 = 10 \sin(2000 \pi t + 2x)$ and $y_2 = 10 \sin(2000 \pi t + 2x + \frac{\pi}{2})$ are superposed at any point at a particular instant. The resultant amplitude is ..... $unit$.

Two coherent sources of sound,$S_{1}$ and $S_{2}$,produce sound waves of the same wavelength,$\lambda = 1\, m$,in phase. $S_{1}$ and $S_{2}$ are placed $1.5\, m$ apart (see figure). $A$ listener,located at $L$,directly in front of $S_{2}$,finds that the intensity is at a minimum when he is $2\, m$ away from $S_{2}$. The listener moves away from $S_{1}$,keeping his distance from $S_{2}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_{1}$. Then,$d$ is $......\, m$.

Two pulses in a stretched string whose centres are initially $8 \ cm$ apart are moving towards each other as shown in the figure. The speed of each pulse is $2 \ cm/s$. After $2 \ seconds$,the total energy of the pulses will be

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times the amplitude of individual motions. The phase difference between the two motions is $.....( ^{\circ)}$

Give noticeable points about the amplitude of resultant waves of two harmonic progressive waves on a stretched string.