FFTW: signal consists of noise after IFFT

Question

After doing FFT and IFFT I can hear only noise in my headphones... Here is the code:

        double* spectrum = new double[n];

        fftw_plan plan;

        plan = fftw_plan_r2r_1d(n, data, spectrum, FFTW_REDFT10, FFTW_ESTIMATE);

        fftw_execute(plan);
        fftw_destroy_plan(plan);

        plan = fftw_plan_r2r_1d(n, spectrum, data, FFTW_REDFT01, FFTW_ESTIMATE);
        fftw_execute(plan);
        fftw_destroy_plan(plan);

Maybe I've chosen wrong FFT type?
P.S. data is the initial signal

UPDATE

Ok, so now the code is

        fftw_complex* spectrum = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n);

        fftw_plan plan;

        plan = fftw_plan_dft_r2c_1d(n, data, spectrum, FFTW_ESTIMATE);

        fftw_execute(plan);
        fftw_destroy_plan(plan);

        plan = fftw_plan_dft_c2r_1d(n, spectrum, data, FFTW_ESTIMATE);
        fftw_execute(plan);
        fftw_destroy_plan(plan);

The problem remains the same, my data array is corrupted.

UPDATE #2

So, the problem is in my transform size and normalizing. If I user real-to-real FFTW_REDFT10 and FFTW_REDFT01 transforms which transform sizes i need to use? 2*n? Or something else? And then I need to normalize my output signal by dividing each element by 2*n?
Thank to all for replying.

UPDATE #3

Thanks to all for replying again. I've solved the problem with your help. Here is the working code:

        // FFT  
        fftw_complex* spectrum  = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * n);

        fftw_plan plan;

        plan = fftw_plan_dft_r2c_1d(n, data, spectrum, FFTW_ESTIMATE);

        fftw_execute(plan);
        fftw_destroy_plan(plan);

        // some filtering here

        // IFFT
        plan = fftw_plan_dft_c2r_1d(n, spectrum, data, FFTW_ESTIMATE);
        fftw_execute(plan);
        fftw_destroy_plan(plan);

        // normalizing

        for (int i = 0; i < n; i++) {
            data[i] = data[i] / n;
        }

Answer 1

I don't see where you are normalizing your output. You must divide your output values by the number of elements in the data array to normalize the data back to original range of values.

See the FFTW Manual 4.8.2, last paragraph (I have V3.2 manual).