Detecting double compressed (DC) speech signals is an important audio forensics task since it is highly related to the integrity and the authenticity of the recording. Adaptive multi-rate (AMR) speech codec is a popular audio compression technique specifically optimized for speech signals and it is a standard audio recording format in the vast majority of the smart phones. All of the previous studies addressing the detection of DC AMR signals report their findings for the speech signals compressed using the narrowband AMR codec (AMR-NB). Meanwhile, wideband AMR codec (AMR-WB) has been used by several mobile phone manufacturers, but DC AMR-WB speech signal detection performance remains unknown. To the best of our knowledge, this is the first study focusing on detecting the DC signals compressed using the AMR-WB speech codec. To this end, we propose three different deep neural network-based DC AMR-WB signal detection systems where the spectrogram representations of the speech signals are used as the input features. Experimental results conducted on TIMIT database provide several important findings regarding the DC AMR-WB speech detection. Firstly, DC AMR-WB detection is found to be a more challenging task than detecting the AMR-NB signals. For example, convolutional neural network (CNN)-based system yields 74.83% and 99.93% detection rates on AMR-WB and AMR-NB coded signals, respectively. Secondly, capturing the temporal information using long short-term memory (LSTM) network with the DC AMR-WB signal detection accuracy of 86.25% is found to be superior to the CNN system. Thirdly, combining the deep feature representations learned by CNN and LSTM networks further improves the performance. Fourthly, the detection rates are found to deteriorate when the signals are first encoded using different audio codecs prior to AMR-WB compression. Finally, applying score level or decision level fusion to the proposed three systems improves the detection rates, in general.