An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the speed of sound and $$\lambda$$ is the wavelength, then the wavelength of the reflected wave $$\lambda_r$$ is

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

When tension $$T$$ is applied to a sonometer wire of length $$I$$, it vibrates with the fundamental frequency $$n$$. Keeping the experimental setup same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency $$n$$. The initial tension applied to the wire (in newton) was

The extension in a wire obeying Hooke's law is $$x$$. The speed of sound in the stretched wire is $$v$$. If the extension in the wire is increased to $$4 x$$, then the speed of sound in a wire is